Solve for $q$, $ -\dfrac{5q + 4}{3q} = -\dfrac{1}{15q} + \dfrac{4}{12q} $
Answer: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $3q$ $15q$ and $12q$ The common denominator is $60q$ To get $60q$ in the denominator of the first term, multiply it by $\frac{20}{20}$ $ -\dfrac{5q + 4}{3q} \times \dfrac{20}{20} = -\dfrac{100q + 80}{60q} $ To get $60q$ in the denominator of the second term, multiply it by $\frac{4}{4}$ $ -\dfrac{1}{15q} \times \dfrac{4}{4} = -\dfrac{4}{60q} $ To get $60q$ in the denominator of the third term, multiply it by $\frac{5}{5}$ $ \dfrac{4}{12q} \times \dfrac{5}{5} = \dfrac{20}{60q} $ This give us: $ -\dfrac{100q + 80}{60q} = -\dfrac{4}{60q} + \dfrac{20}{60q} $ If we multiply both sides of the equation by $60q$ , we get: $ -100q - 80 = -4 + 20$ $ -100q - 80 = 16$ $ -100q = 96 $ $ q = -\dfrac{24}{25}$